一类新的椭圆混合边值问题无穷多正解的存在性

Existence of Infinitely Positive Solutions to a New Elliptic Mixed Boundary Value Problem

研究了一类新的椭圆混合边值问题无穷多正解的存在性,当非线性项f(x,u)关于u在无穷远处满足超线性且满足次临界增长时,利用山路定理证明了该混合边值问题至少存在一个正解.利用迹定理和Sobolev嵌入定理证明了无穷多正解存在性定理.

The existence of infinitely positive solutions to a new elliptic mixed boundary value problem has been studied. When nonlinear term f（x, u） is super-linear with respect to at infinity, and f（x,u） is subcritical growth, the mixed boundary value problem has at least one positive solution, which is proved by Mountain Pass Theorem. Furthermore, the trace theorem and Sobolev embedding theorem are applied to the proof of the existence of positive solutions.